My question is :
- Take $n + 1$ numbers out of $1, 2,..., 2n$
- Show that there will be two consecutive numbers
My Approach :
- Using the Pigeon Hole Principle , the $n$ holes are labelled $(1, 2), (3, 4), . . ., (2n − 1, 2n)$
- A chosen number $k$ goes into hole $(j, j + 1)$ exactly if $k ∈ (j, j + 1)$
Am I correct ? Help would be appreciated !